Enforcing safety while preventing overly conservative behaviors is essential for autonomous vehicles to achieve high task performance. In this paper, we propose a barrier-enhanced parallel homotopic trajectory optimization (BPHTO) approach with the over-relaxed alternating direction method of multipliers (ADMM) for real-time integrated decision-making and planning. To facilitate safety interactions between the ego vehicle (EV) and surrounding vehicles, a spatiotemporal safety module exhibiting bi-convexity is developed on the basis of barrier function. Varying barrier coefficients are adopted for different time steps in a planning horizon to account for the motion uncertainties of surrounding HVs and mitigate conservative behaviors. Additionally, we exploit the discrete characteristics of driving maneuvers to initialize nominal behavior-oriented free-end homotopic trajectories based on reachability analysis, and each trajectory is locally constrained to a specific driving maneuver while sharing the same task objectives. By leveraging the bi-convexity of the safety module and the kinematics of the EV, we formulate the BPHTO as a bi-convex optimization problem. Then constraint transcription and the over-relaxed ADMM are employed to streamline the optimization process, such that multiple trajectories are generated in real time with feasibility guarantees. Through a series of experiments, the proposed development demonstrates improved task accuracy, stability, and consistency in various traffic scenarios using synthetic and real-world traffic datasets.

翻译：在确保安全的同时避免过度保守行为对于自动驾驶车辆实现高任务性能至关重要。本文提出一种基于超松弛交替方向乘子法（ADMM）的障碍增强型并行同伦轨迹优化（BPHTO）方法，用于实现实时集成决策与规划。为促进主车（EV）与周围车辆的安全交互，基于障碍函数构建了具有双凸特性的时空安全模块。在规划时域内针对不同时间步采用可变的障碍系数，以考虑周围人类驾驶车辆（HV）的运动不确定性并缓解保守行为。此外，我们利用驾驶行为的离散特性，基于可达性分析初始化面向标称行为的自由终端同伦轨迹簇，每条轨迹在共享相同任务目标的同时被局部约束于特定驾驶行为。通过利用安全模块的双凸特性和主车运动学模型，将BPHTO问题构建为双凸优化问题。随后采用约束转录技术与超松弛ADMM算法来简化优化过程，从而在保证可行性的前提下实时生成多条轨迹。通过一系列实验，基于合成与真实交通数据集的测试表明，所提方法在多种交通场景中均展现出更高的任务精度、稳定性与一致性。